Issolvi sqrt{(6sqrt{6})^2+(6sqrt{2})^2}

$$\sqrt { ( 6 \sqrt { 6 } ) ^ { 2 } + ( 6 \sqrt { 2 } ) ^ { 2 } }$$

Evalwa

$$12\sqrt{2}\approx 16.970562748$$

Passi tas-Soluzzjonijiet

Espandi \left(6\sqrt{6}\right)^{2}.

$$\sqrt{6^{2}\left(\sqrt{6}\right)^{2}+\left(6\sqrt{2}\right)^{2}}$$

Ikkalkula 6 bil-power ta' 2 u tikseb 36.

$$\sqrt{36\left(\sqrt{6}\right)^{2}+\left(6\sqrt{2}\right)^{2}}$$

Il-kwadrat ta' \sqrt{6} huwa 6.

$$\sqrt{36\times 6+\left(6\sqrt{2}\right)^{2}}$$

Immultiplika 36 u 6 biex tikseb 216.

$$\sqrt{216+\left(6\sqrt{2}\right)^{2}}$$

Espandi \left(6\sqrt{2}\right)^{2}.

$$\sqrt{216+6^{2}\left(\sqrt{2}\right)^{2}}$$

Ikkalkula 6 bil-power ta' 2 u tikseb 36.

$$\sqrt{216+36\left(\sqrt{2}\right)^{2}}$$

Il-kwadrat ta' \sqrt{2} huwa 2.

$$\sqrt{216+36\times 2}$$

Immultiplika 36 u 2 biex tikseb 72.

$$\sqrt{216+72}$$

Żid 216 u 72 biex tikseb 288.

$$\sqrt{288}$$

Iffattura 288=12^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{12^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{12^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 12^{2}.

$$12\sqrt{2}$$